Experiment 2: The production of L3 vowels in absolute beginners
The purpose of experiment 1 was to evaluate VOT in beginning L3 learners in each of their known languages and their new language to determine cross-linguistic interactions. Experiment 2 has the same agenda, but instead of VOT, vowels are examined to determine how cross-linguistic interactions may occur. Ideally, an analysis of the same tokens as experiment 1 will be used for experiment 2.
Notes and troubles
This is an overview of my initial proposal for experiment 2.
The central purpose of experiment 2 is to evaluate the production of the L3 vowel space of absolute L3 beginners (i.e. sequential bilinguals after their first exposure to a third language), and to determine whether the L3 vowel space is more L1 or L2 like. The justification for this experiment is to provide more robust evidence that may be used in the evaluation of the predictions of L3 models. Long-form justifications and previous literature will be covered in the formal dissertation proposal.
Research Question
Will absolute beginners produce vowels in a third language at first exposure more like (a) L1 vowels, (b) L2 vowels, or (3) L3 vowels that they are exposed to in the experiment?
Methods
Questionnaire used in the pilot
Questionnaire used in the pilot
Goal: Elicit production of L1, L2 and L3 words containing copmparable vowels for analysis.
These elicitation methods are flexible, since they’re not incredibly driven by theory - I am not opposed to using a carrier sentence in each language if I can avoid co-articulation effects and if it seems reasonable that the speakers could learn an L3 carrier sentence
Task: Shadowing Task
Task: Elicited Production task
Spanish-English bilinguals will produce word lists in isolation in their L1, L2 and an L3 that they do not know. For the L3, they will complete a shadowing task (training), in which they will listen L3 words one at a time and repeat them aloud. Following the shadowing task, the participants will then complete 3 elicited production tasks in their L1 and L2 (the order will be counter-balanced), and all participants will finish with the EPT in the L3.
Tokens will be extracted from these productions an analyzed in PRAAT.
Undecided
Give all participants the same L3, or divide it in some way. If many L3s were given then it could be added to the model to see whether language given makes a difference in the use of L1 or L2. But would I need 5x as many experiments?
If just one language: German
The German vowel space is huge https://en.wikipedia.org/wiki/Standard_German_phonology#CITEREFDudenredaktionKleinerKnöbl2015
new vowel sounds *
Will L3 learners assimilate L3 vowel sounds to L1 or L2 sounds?
L1 /e/, L2 /e/, L3 /e/, L3 /novel/
German:
Participants
200 total participants will take part in the experiment. The participants will be Spanish-English bilinguals, with both English L1 (n = 100), and Spanish L1 (n = 100).
Materials
Stimuli:
4 repetitions of each vowel in each language. 20x words per language.
Analysis
The data were analyzed using two Bayesian generalized multilevel regression models in R. The models were fit using the rstanglmer function in the rstanarm package.
The models’ outcome variable was F1 and F2 respectively and was measured in Hertz. In each mode, the formant was modeled as a function of vowel, language, and the vowel and language interaction. The categorical variables of language and vowel were both dummy coded. The random effects structure included by-participant random intercepts and slopes for language and vowel. The priors were the rstanglmer function default of weakly informative priors. Due to the fact that the research question of the present study aims to establish practical equivalence between languages, the region of practical equivalence was set to a medium effect size (Cohen’s < .5). As a result, if the distribution of the posterior parameter estimates is less than .5 standard deviations away from the reference value, that distribution would fall inside the region of practical equivalence, and would be assumed to be equivalent.
Materials
Simulated Data and results
The Simulated Data
Data were simulated in R using the rnorm function for each vowel for both the first and second formant, in each the L1, L2 and L3 for 100 participants, with each vowel being repeated 4 times. As a result, 20 tokens (4 repititions x 5 vowels) were simulated per language for 100 total participants, totaling 2000 observations per language (100 participants x 20 tokens). Thus, in total, the simulated dataset contained 6000 observations for both F1 and F2. The mean formant values for F1 and F2 were adapted from the monolingual values reported in Bradlow (1995), and the L3 values were simulated to closely resemble the L2 values in order to demonstrate what would be interpreted as L2-like L3 vowel productions in the statistical models. The script used to simulate the dataset can be found under scripts and is titled 01_simdata.R.
The Simulated Results
The design of the present study sets L3 as the reference level in a bayesian generalized linear regression model. As a result, the interpretation of the forest plots is relatively straight forward; if a distribution of plausible parameter estimates falls entirely within the determined region of practical equivalence (ROPE; the dashed, vertical lines on the forest plot), then it will be taken as evidence for the use of L1 or L2 phonology at the first exposure to the L3. The results of the simulated bayesian analyses showed evidence of practical equivalence between the L2 and L3 for all vowels in F1, and a similar trend, though it appears less clear, in the F2 model.
The figures are forest plots of the parameter estimates of each vowel x language interaction from the Bayesian regression model. The reference level for language was L3 and /a/ for vowel.
| mean | mcse | sd | 10% | 50% | 90% | n_eff | Rhat | |
|---|---|---|---|---|---|---|---|---|
| (Intercept) | 626.883771 | 0.0600036 | 2.542555 | 623.669823 | 626.864009 | 630.189368 | 1796 | 1.001730 |
| languagel1 | 154.048201 | 0.0806336 | 3.556170 | 149.477464 | 154.028695 | 158.633228 | 1945 | 1.001318 |
| languagel2 | 9.001054 | 0.0809350 | 3.522648 | 4.467497 | 8.989771 | 13.524665 | 1894 | 1.001644 |
| vowele | -206.932682 | 0.0740890 | 3.543371 | -211.467077 | -206.880170 | -202.509388 | 2287 | 1.001068 |
| voweli | -368.981921 | 0.0727442 | 3.583411 | -373.524034 | -369.017861 | -364.385027 | 2427 | 1.000541 |
| vowelo | -155.772187 | 0.0751139 | 3.618171 | -160.487173 | -155.775150 | -151.201372 | 2320 | 1.000592 |
| vowelu | -307.080678 | 0.0714725 | 3.611789 | -311.738174 | -307.046869 | -302.476818 | 2554 | 1.001104 |
| languagel1:vowele | -116.587258 | 0.0996713 | 4.991129 | -122.964438 | -116.567444 | -110.187707 | 2508 | 1.000573 |
| languagel2:vowele | -3.428371 | 0.1038241 | 4.998551 | -9.689918 | -3.411964 | 3.072472 | 2318 | 1.000215 |
| languagel1:voweli | -125.711035 | 0.0988099 | 4.998842 | -132.104786 | -125.753088 | -119.376112 | 2559 | 1.000906 |
| languagel2:voweli | -3.683557 | 0.0992193 | 5.101428 | -10.149787 | -3.604455 | 2.759617 | 2644 | 1.000366 |
| languagel1:vowelo | -167.027215 | 0.0984998 | 5.088994 | -173.455541 | -167.102394 | -160.586584 | 2669 | 1.000295 |
| languagel2:vowelo | -7.737827 | 0.1032165 | 5.020612 | -14.187380 | -7.660635 | -1.381260 | 2366 | 1.001338 |
| languagel1:vowelu | -152.276683 | 0.1004567 | 5.094717 | -158.817991 | -152.230761 | -145.778577 | 2572 | 1.001225 |
| languagel2:vowelu | -12.470140 | 0.0980973 | 4.993016 | -18.823570 | -12.444017 | -5.976336 | 2591 | 1.001323 |
| mean | mcse | sd | 10% | 50% | 90% | n_eff | Rhat | |
|---|---|---|---|---|---|---|---|---|
| (Intercept) | 1337.549651 | 0.0874525 | 4.842924 | 1331.399611 | 1337.572879 | 1343.8035212 | 3067 | 0.9999594 |
| languagel1 | -154.101098 | 0.1243757 | 6.897010 | -162.990756 | -154.100569 | -145.1695653 | 3075 | 0.9998745 |
| languagel2 | 16.789555 | 0.1157789 | 6.846372 | 7.942777 | 16.793484 | 25.6146328 | 3497 | 0.9999727 |
| vowele | 681.393595 | 0.1126351 | 6.899335 | 672.514195 | 681.506844 | 690.3557746 | 3752 | 0.9994094 |
| voweli | 922.777552 | 0.1122442 | 6.825494 | 913.868800 | 922.883724 | 931.5302985 | 3698 | 1.0011651 |
| vowelo | -246.801309 | 0.1099623 | 6.826517 | -255.631554 | -246.712566 | -237.9524200 | 3854 | 1.0000369 |
| vowelu | -157.189483 | 0.1120610 | 6.926181 | -166.062130 | -157.063191 | -148.2928068 | 3820 | 1.0005742 |
| languagel1:vowele | -54.488124 | 0.1555199 | 9.572193 | -66.458562 | -54.506744 | -41.7569904 | 3788 | 0.9997046 |
| languagel2:vowele | -5.420253 | 0.1546193 | 9.663152 | -17.853931 | -5.549375 | 6.8920949 | 3906 | 0.9995089 |
| languagel1:voweli | -206.312948 | 0.1619502 | 9.756602 | -218.819289 | -206.319386 | -193.7348977 | 3629 | 0.9996907 |
| languagel2:voweli | -17.446642 | 0.1522872 | 9.549300 | -29.605390 | -17.513071 | -5.5063070 | 3932 | 1.0003627 |
| languagel1:vowelo | 75.911884 | 0.1558844 | 9.703118 | 63.359610 | 75.772109 | 88.0988882 | 3875 | 1.0000456 |
| languagel2:vowelo | -13.077439 | 0.1499778 | 9.393698 | -25.131951 | -13.179899 | -0.7514183 | 3923 | 0.9995231 |
| languagel1:vowelu | -37.617345 | 0.1586248 | 9.672907 | -50.219004 | -37.712896 | -25.0521722 | 3719 | 1.0000097 |
| languagel2:vowelu | -18.690507 | 0.1526614 | 9.537875 | -31.019146 | -18.636209 | -6.2739405 | 3903 | 1.0009701 |
